Digital signal processing requires converters for converting the signals of the surrounding analog world into digital form and then again from digital to analog form, that is, analog-to-digital (A/D) and digital-to-analog (D/A) converters. Oversampled converters are used in many (e.g. audio-) applications to improve performance. Among such oversampled converters, so-called sigma-delta converters enabling advantageous implementation technology have been paid plenty of attention. Sigma-delta converters are described e.g. in OversampIed A/D and D/A Converters for VLSI System Integration by T. Ritoniemi, V. Eerola, T. Karema and H. Tenhunen, Proc. IEEE ASIC Seminar and Exhibit, Sep. 1990, P8-7.1.-P8.7.12.
The sigma-delta D/A converter comprises three different stages: an interpolation filter, a noise shaper, i.e. a digital sigma-delta modulator, and a reconstruction filter. In the interpolation filter, the number of samples representing the signal is increased by digital filtration. In the sigma-delta modulator, incoming samples are approximated by one bit. In the reconstruction filter, a single-bit D/A conversion is performed, and the obtained analog signal is filtered by an analog filter to remove frequency components outside of the signal band (such as the quantization noise of the modulator).
The digital sigma-delta modulator comprises one or more cascaded integration stages. The sign of the output of the last integration stage, delayed by one sample and multiplied by a suitable scaling coefficient, is combined with the input signal of each integration stage. The scaling coefficients are selected so that the modulator is stable. The order of the sigma-delta modulator is determined by the number of the integration stages. By using a higher order modulator, the precision can be improved while the interpolation ratio remains unchanged.
A problem with prior art sigma-delta modulators is, however, that the spectrum of the modulator is not such as desired in all situations but the bit sequence generated at the output of the modulator easily starts to repeat the same bit pattern with resulting undesired frequency components, that is, limit cycle oscillation.
A similar phenomenon is known to occur in a conventional digital filter during zero-value input due to rounding or truncation noise (Discrete-Time Signal Processing, A.V. Oppenheimer and R.W. Schafer, Prentice Hall, 1989). The sigma-delta modulator is, however, a strongly non-linear system in which the feedback is established on the basis of the sign of the output signal, and the value feedbacked to the first integration stage is always higher than the value of the input signal. The sigma-delta modulator thus behaves in a completely different way than a conventional digital filter, which is a linear system. In the sigma-delta modulator, limit cycle oscillation may actually occur at all input values.
Limit cycle oscillation is also known to occur in the modulator of a first-order sigma-delta A/D converter (Analog to Digital Conversion Using Sigma-Delta Modulation and Digital Signal Processing, J.R. Fox and J.G. Garrison, Conference on Advanced Research in VLSI M.I.T., 1982, p. 101-112), in which the problem has been solved by combining a so-called jitter signal having a frequency outside of the signal band with the analog input signal of the single integration stage. Due to the added jitter signal, the input is always active, and no undesired frequencies occur at small input values. The jitter signal is filtered off in a decimation filter because its frequency is outside of the signal band. In addition, both signals to be combined are analog, and so they are easy to combine.
In the sigma-delta D/A converter, all signals are multi-bit digital signals, wherefore the combining of a jitter signal of a predetermined frequency with the input signal should be carried out similarly as with multi-bit digital signals. The multi-bit adder required for the purpose would limit the operating frequency of the modulator, increase the power consumption and require plenty of surface area on the silicon substrate when the modulator is realized as an integrated circuit.